Lenses and prisms are refracting optical elements configured to adjust the energy distribution of transmitted electromagnetic radiation. Most simple lenses are configured with two surfaces that correspond to surfaces of a sphere, where each surface can be manufactured as a convex surface (i.e., bulging outward from the lens), a concave surface (i.e., depressed into the lens), or a planar surface. For example, FIG. 1A shows side views of a biconvex lens 102, a biconcave lens 104, and plano-convex lens 106. The biconvex lens 102 comprises two opposing convex surfaces, the biconcave lens 104 comprises two opposing concave surfaces, and the plano-convex lens 106 comprises opposing convex and planar surfaces. As shown in FIG. 1B, a collimated beam of electromagnetic radiation 108 travelling parallel to the optical axis 110 and passing through the biconvex lens 102 converges or is said to be focused to a spot called the focal point 112 on the optical axis 110, at a certain distance behind the lens. This distance is called the focal length, and the lens 102 is also referred to as a positive or converging lens. On the other hand, FIG. 1C shows a collimated beam of electromagnetic radiation 114 passing through the biconcave lens 104. The beam after passing through the lens 104 diverges or spreads out and appears to be emanating from a point, also called a focal point 116, on the optical axis 118 in front of the lens 104. The distance from the point 116 to the center of the lens 104 is also known as the focal length, although it is negative with respect to the focal length of a convex lens.
Because simple lenses can be manufactured with various convex and concave curvatures, lenses are among the most widely and commonly used optical elements. For example, a simple lens can be configured as a corrective lens in eye glasses or a lens of a magnifying glass. On the other hand, a compound lens is an arrangement of simple lenses that share a common optical axis. The simple lenses of a compound lens can be configured and spaced along the optical axis to correct for optical aberrations and to magnify images of small or distant objects in devices such as microscopes, camera lenses, and telescopes in ways that are not possible using only a simple lens.
A prism, on the other hand, is a transparent optical element with flat, polished surfaces that refract transmitted electromagnetic radiation. The exact angles between the surfaces depend on the application and the desired degree to which the transmitted electromagnetic radiation is bent. Prisms can be manufactured with traditional geometrical shapes, such as a triangular prism with a triangular base and top and rectangular sides.
Manufactured optical elements are typically composed of glass or a transparent plastic and may be cut, ground, and polished after manufacturing to change the optical properties, such as changing the optical axis, focal point, focal length, degree of refraction, or whether the lens is convergent or divergent. For example, a lens can be cut, ground, and polished after manufacturing to change the focal length or to reposition the optical axis to no longer pass through the physical center of the lens. However, changing the optical properties of an optical element is typically a labor intensive process that fixes the optical properties of the optical element. After the optical properties of a manufactured lens have been changed via cutting and grinding, it may be too labor intensive or impossible to restore the lens to its original manufactured optical properties. For example, it may be impossible to reconfigure a biconvex lens as a prism or as a biconcave lens via cutting and grinding.
Thus, it is desirable to have optical devices that can be operated as reconfigurable optical elements.